CN113193798A - Method for driving a star-connected three-phase electric machine - Google Patents

Abstract

The invention relates to a method for driving a star-connected three-phase electric machine. A method of driving a three-phase motor includes driving a second phase using a sinusoidal first drive function when a first phase is energized. The first phase is switched to a non-energized state, and a back electromotive force (BEMF) voltage of the first phase is detected. The driving of the second phase is dependent on the output of a second drive function different from the first drive function for at least a portion of the time when the first phase is not energized. The second drive function may be a non-sinusoidal function and may be a cosine function. The second drive function may drive the second phase when the output of the second drive function is a modulation ratio less than 1. When the output of the second drive function is a modulation ratio greater than or equal to 1, the second phase may be driven to a modulation ratio of 1.

Description

Method for driving a star-connected three-phase electric machine

Technical Field

Aspects of this document relate generally to a method of controlling a three-phase motor. Particular aspects of this document relate to a method of controlling a star-connected three-phase sensorless motor.

Background

Three-phase motors use power applied to the motor in three different phases to rotate the motor. These phases usually involve separate electrical connections and are usually referred to as U-phase, V-phase and W-phase.

Disclosure of Invention

Embodiments of a method of driving a wye-connected three-phase motor may include: driving a second phase of the three-phase motor using a first sinusoidal drive function when the first phase of the star-connected three-phase motor is in an energized state; and switching the first phase to a non-energized state. The method may also include detecting a first back electromotive force (BEMF) voltage of the first phase when the first phase is in a non-energized state; and driving the second phase using a second drive function different from the first sinusoidal drive function for at least a portion of the time when the first phase is in the non-energized state.

Embodiments of the method of driving a star-connected three-phase electric machine may include one, all or any of the following:

the three-phase motor may be a sensorless brushless direct current (BLDC) motor or a Permanent Magnet Synchronous Motor (PMSM).

The method may include wherein driving the second phase using the second drive function results in an increase in voltage applied to the second phase relative to driving the second phase using the first sinusoidal drive function.

The method may include wherein a third phase of the three-phase motor may be driven using a third drive function different from the second sinusoidal drive function when the first phase is in the second unenergized state.

The method may include wherein driving the third phase using the third drive function results in an increase in voltage applied to the third phase relative to driving the third phase using the second sinusoidal drive function.

The method may include wherein after driving the second phase using the second drive function until the first BEMF voltage is detected, the second phase may be driven using the first sinusoidal drive function.

The method may include wherein after driving the second phase using the second drive function for a predetermined amount of time, the second phase may be driven using the first sinusoidal drive function.

In an embodiment of the method, plotting the generated torque of the three-phase motor on the y-axis and plotting the rotor angular position of the rotor of the three-phase motor on the x-axis may show that there is no change in the generated torque over 360 degrees of rotation of the rotor for at least one electric drive.

Embodiments of a method of driving a wye-connected three-phase motor may include: driving a first phase of a star-connected three-phase motor using a first sinusoidal drive function when all three phases are energized; the first phase is driven using the first non-sinusoidal drive function for at least a portion of the time when a phase other than the first phase is not energized and when the first non-sinusoidal drive function produces a modulation ratio less than 1. The method may include driving the first phase to a modulation ratio of 1 for at least a portion of the time when a phase other than the first phase is not energized and when the first non-sinusoidal drive function produces a modulation ratio greater than or equal to 1.

Embodiments of the method of driving a star-connected three-phase electric machine may include one, all or any of the following:

the modulation ratio may be a low torque ripple modulation ratio.

The first non-sinusoidal drive function may be a first cosine drive function.

The first cosine drive function may be

Wherein M is a modulation ratio of 0 to 1, wherein θ is a rotation angle of the three-phase motor, and wherein θ_wcWhen θ is less than 30 degrees and greater than or equal to 0 degrees, it has a value of 0 degrees, when θ is less than 90 degrees and greater than or equal to 30 degrees, it has a value of 60 degrees, when θ is less than 150 degrees and greater than or equal to 90 degrees, it has a value of 180 degrees, when θ is less than 210 degrees and greater than or equal to 150 degrees, it has a value of 240 degrees, when θ is less than 270 degrees and greater than or equal to 210 degrees, it has a value of 300 degrees, when θ is less than 330 degrees and greater than or equal to 270 degrees, and when θ is less than 360 degrees and greater than or equal to 330 degrees, it has a value of 0 degrees.

The first sinusoidal drive function may be

Wherein

Where M is a modulation ratio of 0 to 1, and where θ is a rotation angle of the three-phase motor.

Embodiments of the method may include wherein when all three phases are energized, a second phase of the three-phase motor may be driven using a second sinusoidal drive function; driving the second phase using the first non-sinusoidal drive function during at least a portion of the time when a phase other than the second phase is not energized and when the first non-sinusoidal drive function produces a modulation ratio less than 1; and the second phase may be driven to a modulation ratio of 1 during at least a portion of the time when a phase other than the second phase is not energized and when the first non-sinusoidal drive function produces a modulation ratio greater than or equal to 1.

The second sinusoidal drive function may be

Wherein

Where M is a modulation ratio of 0 to 1, and where θ is a rotation angle of the three-phase motor.

Embodiments of the method may include wherein when all three phases are energized, a third phase of the three-phase motor may be driven using a third sinusoidal drive function; driving the third phase using the first non-sinusoidal drive function during at least a portion of when a phase other than the third phase is not energized and when the first non-sinusoidal drive function produces a modulation ratio less than 1; and the third phase may be driven to a modulation ratio of 1 during at least a portion of the time when a phase other than the third phase is not energized and when the first non-sinusoidal drive function produces a modulation ratio greater than or equal to 1.

The third sinusoidal drive function may be

Wherein

Where M is a modulation ratio of 0 to 1, and where θ is a rotation angle of the three-phase motor.

Embodiments of a method of driving a three-phase motor may include: when all three phases are electrified, driving the U phase of the three-phase motor by using a first sinusoidal driving function; when all three phases are electrified, driving the V phase of the three-phase motor by using a second sinusoidal driving function; when all three phases are electrified, driving the W phase of the three-phase motor by using a third sinusoidal driving function; and driving the two of the three phases that are energized using a cosine drive function for at least a portion of the time that is not energized during a period when one of the three phases is not energized.

Embodiments of the method of driving a three-phase motor may include one, all or any of the following:

the modulation ratio may be a low torque ripple modulation ratio.

In various embodiments of the method, the energized two of the three phases may be driven using the cosine drive function during a period when one of the three phases is not energized and during at least a portion of the time when the cosine drive function produces a modulation ratio less than 1, and the energized two of the three phases may be driven to a modulation ratio of 1 during a period when one of the three phases is not energized and during at least a portion of the time when the cosine drive function produces a modulation ratio greater than or equal to 1.

The cosine drive function may be

Wherein M is a modulation ratio of 0 to 1, wherein θ is a rotation angle of the three-phase motor, and wherein θ_wcWhen theta is less than 30 degrees and greater than or equal to 0 degree, has a value of 0 degree, when theta is less than 90 degrees and greater than or equal to 30 degrees, has a value of 60 degrees, when theta is less than 150 degrees and greater than or equal to 90 degrees, has a value of 120 degrees, when theta is less than 210 degrees and greater than or equal to 150 degrees, has a value of 180 degrees, when theta is less than 270 degrees and greater than or equal to 210 degrees, has a value of 0 degreesThere is a value of 240 degrees, a value of 300 degrees when theta is less than 330 degrees and greater than or equal to 270 degrees, and a value of 0 degrees when theta is less than 360 degrees and greater than or equal to 330 degrees.

The first sinusoidal drive function may be

The second sinusoidal drive function may be

And the third sinusoidal drive function may be

Wherein

Where M is a modulation ratio of 0 to 1, and where θ is a rotation angle of the three-phase motor.

The above and other aspects, features and advantages will be apparent to those of ordinary skill in the art from the detailed description and drawings, and from the claims.

Drawings

Embodiments will hereinafter be described in conjunction with the appended drawings, wherein like designations denote like elements, and:

FIG. 1 is a graph of voltage and current magnitudes plotted as a function of electrical angle position of a rotor for a particular implementation of a method of driving a three-phase motor;

FIG. 2 is a torque graph illustrating torque ripple plotted as a function of electrical angular position of the rotor for the method of FIG. 1;

FIG. 3 is a graph of voltage and current magnitudes plotted as a function of electrical angle position of the rotor for a particular implementation of a method of driving a three-phase motor;

FIG. 4 is a graph of torque plotted against electrical angular position of the rotor for the method of FIG. 3;

FIG. 5 is a graph of torque plotted against electrical angular position of the rotor for a method of driving a three-phase motor;

FIG. 6 is a graph of a Lissajous curve for the method of FIG. 3;

FIG. 7 is a graph of a Lissajous curve for a method similar to that of FIG. 3, except that a modulation ratio of 0.7 is used;

fig. 8 is a schematic diagram illustrating control of the U-phase in a method of driving a three-phase motor;

fig. 9 is a schematic diagram illustrating control of the U-phase in a method of driving a three-phase motor;

fig. 10 is a schematic diagram showing control of the U-phase in the method of driving the three-phase motor;

fig. 11 is a schematic diagram illustrating control of the U-phase in a method of driving a three-phase motor;

fig. 12 is a schematic diagram showing control of the U-phase in the method of driving the three-phase motor;

fig. 13 is a schematic diagram showing control of the U-phase in the method of driving the three-phase motor;

fig. 14 is a schematic diagram showing control of the V phase in the method of driving the three-phase motor;

fig. 15 is a schematic diagram showing control of the V phase in the method of driving the three-phase motor;

fig. 16 is a schematic diagram showing control of the U-phase in the method of driving the three-phase motor;

fig. 17 is a schematic diagram illustrating control of the V phase in the method of driving the three-phase motor;

fig. 18 is a diagram showing windows for detecting BEMF signals of U-phase, V-phase, and W-phase in a method of driving a three-phase motor;

fig. 19 is a diagram showing windows for detecting BEMF signals of U-phase, V-phase, and W-phase in a method of driving a three-phase motor;

fig. 20 is a diagram showing windows for detecting BEMF signals of U-phase, V-phase, and W-phase in a method of driving a three-phase motor;

fig. 21 is a schematic diagram of current vectors in a method of driving a three-phase motor;

FIG. 22 is a graph of voltage and current magnitudes plotted as a function of electrical angle position of the rotor for a particular implementation of a method of driving a three-phase motor;

FIG. 23 is a graph of voltage and current magnitudes plotted as a function of electrical angle position of the rotor for a particular implementation of a method of driving a three-phase motor;

FIG. 24 is a graph of torque plotted as a function of electrical angular position of the rotor for the method of FIG. 22;

FIG. 25 is a torque graph illustrating the absence of torque ripple plotted against the electrical angular position of the rotor for the method of FIG. 23;

FIG. 26 is a graph of a Lissajous curve for the method of FIG. 22;

FIG. 27 is a graph of a Lissajous curve for the method of FIG. 23;

FIG. 28 is a graph of voltage and current magnitudes plotted as a function of electrical angle position of the rotor for a particular implementation of a method of driving a three-phase motor;

FIG. 29 is a graph of voltage and current magnitudes plotted as a function of electrical angle position of the rotor for a particular implementation of a method of driving a three-phase motor;

FIG. 30 is a torque graph illustrating the absence of torque ripple plotted against the electrical angular position of the rotor for the method of FIG. 29;

FIG. 31 is a graph of a Lissajous curve for the method of FIG. 29;

fig. 32 is a circuit diagram representatively showing a circuit of a controller for controlling the three-phase motor;

fig. 33 is a block diagram representatively illustrating a controller for controlling the three-phase motor;

fig. 34 is a timing diagram of a method of controlling a three-phase motor;

FIG. 35 is a timing diagram of a method of controlling a three-phase motor;

fig. 36 is a timing chart of a method of controlling a three-phase motor; and is

Fig. 37 is a block diagram representatively illustrating a three-phase motor and elements for controlling the three-phase motor and detecting the BEMF signal.

Detailed Description

The present disclosure, aspects, and embodiments thereof, are not limited to the specific components, assembly processes, or method elements disclosed herein. Many additional components, assembly procedures, and/or method elements known in the art to be consistent with the intended drive method of a three-phase electric machine will be readily apparent for use with particular embodiments of the present disclosure. Thus, for example, although specific embodiments are disclosed herein, such embodiments and implementation components may include any shape, size, style, type, model, version, measurement, concentration, material, quantity, method element, step, etc. of such driving methods and implementation components and methods known in the art for three-phase motors consistent with the intended operation and method.

During operation of a three-phase motor, such as at start-up and at other times during operation, the motor controller needs to detect the position and rotational speed of the rotor of the motor. Accurately doing so may allow for precise motor control by adjusting the timing of the supply voltage applied to the motor windings. In some motors, hall sensors may be used to detect rotor position, but for sensorless motors, a back electromotive force (BEMF) signal may be used to detect the position, such as by comparing the BEMF signal to a voltage to determine when the motor crosses zero.

During BEMF detection, the phase used to detect the BEMF signal may be temporarily de-energized, causing a change in output torque, referred to as a "torque ripple. The output torque of the electric machine may vary continuously between two or more values due to torque fluctuations. Torque ripple can generally affect the performance of the motor, reduce motor efficiency, increase noise generated by the motor, increase wear of motor components, and reduce the life of the motor components and the motor.

The method disclosed herein includes a three-phase motor modulation method that improves drive torque ripple. Each phase of a three-phase motor represents one of the windings of the motor stator. In particular implementations, the method may improve drive torque ripple in an N-window drive method. The N-window driving method is a method including a window in which one phase is not excited when a phase BEMF voltage of the phase is detected. While different types of three-phase motors may benefit from the methods disclosed herein, one example of a motor that may be driven using the methods disclosed herein is a star-connected three-phase brushless direct current (BLDC) motor. Another example is a star-connected three-phase permanent magnet synchronous machine (PMSM or SPMSM). To perfectly compensate for the reduced torque during BEMF sensing, methods such as strict Field Orientation Control (FOC) (vector control) may be applied. The methods disclosed herein do not use vector control and may be useful for situations where it is desirable to ameliorate (reduce/eliminate) torque ripple but perfect compensation is not required and/or vector control is too expensive or otherwise infeasible. The method disclosed herein includes using an algorithm for driving a three-phase motor, which may be controlled by one or more integrated circuits. In one example, the integrated circuit is a Field Programmable Gate Array (FPGA), but in other embodiments, other programmable and non-programmable (i.e., ASIC) circuit types may be used.

For an N-window drive system in which the phase BEMF voltage of one of the three phases is not excited when detected, the system cannot apply a desired drive torque vector to the motor due to the non-excited phase, and the motor operation includes torque ripple.

Referring now to fig. 1, a graph representing control of a three-phase motor includes voltage and current magnitudes plotted against the electrical angular position of the rotor of the motor. The drive voltage amplitude (U2pm, V2pm, W2pm, where U, V and W are phases and 2pm represents a two-phase modulation with a non-excited phase) represents the motor terminal voltage and is plotted using lines, dashed lines and dotted lines, respectively. The phase drive current magnitudes (IU, IV, and IW) represent the phase currents (motor stator currents) and are plotted using squares, triangles, and circles, respectively. For simplicity, the stator inductance and BEMF voltage are omitted for ease of viewing other details of the graph. The electrical angular position of the rotor is given in radians. As can be seen from the current amplitudes, the current for each phase is approximately sinusoidal, but for each phase there is a window in which the current is intentionally zero over a period of time. This is an N-window and may otherwise be referred to as the HiZ (high impedance) state of the phase. For example, when the U-phase is in a zero-phase current window (N-window or HiZ-window), BEMF zero-crossings may be determined for determining the rotor position of the electric machine. During this HiZ window, the torque of the motor is reduced, resulting in the torque ripple previously discussed. It should be noted that where the current is substantially sinusoidal, the applied voltage amplitude is also substantially sinusoidal, except at the HiZ window. In this example, a modulation ratio of 0.6 is used.

Fig. 2 representatively illustrates torque of the three-phase electric machine of fig. 1 plotted against electrical degrees (this time in degrees) of the rotor of the machine. The torque is represented by a q-axis current converted by the clark-park transformation, which represents the torque produced. The torque ripple can be seen in fig. 2, where the torque drops very low in several places, each of these drops corresponding to the HiZ window of one of the phases.

Fig. 3 shows another example of a graph of voltage and current magnitude plotted against electrical angle position for an N-window drive method. The features/details of the graph are similar to those described above with respect to fig. 1, except for the values plotted. In this example, the phase currents are again considered to be relatively sinusoidal, but with a HiZ period in which the current is intentionally zero for a period of time. The graph of fig. 3 includes a window 2 indicating a period in which the phase BEMF voltage is detected using the non-excited phase. The driving method of fig. 3 uses a modulation ratio of 1.0.

Fig. 4 representatively illustrates torque plotted against an electrical angular position of the rotor for the driving method of fig. 3. The features/details of the graph are similar to those described above with respect to fig. 2, except for the plotted values. Torque ripple is again visible. The window 4 shown on the graph is aligned with the torque ripple, which can be seen to correspond to the HiZ window, and also aligned with the HiZ window 2 of fig. 3. Fig. 5 shows a torque diagram for a driving method similar to that of fig. 3, except that the driving method uses a modulation ratio of 0.7. The torque ripple is still visible in the window 6, which corresponds to the HiZ window of the driving method in which the phase BEMF voltage is detected.

Fig. 6 shows lissajous curves of drive current converted by the clarke transform for the drive method of fig. 3 using a modulation ratio of 1.0. The I-Alpha axis is Alpha axis current and the I-Beta axis is Beta axis current. The lissajous curve shows the position of the torque when current is applied and the motor is applied. At locations where there are no circles on the curve, this indicates that the torque jumps from one value to another — these locations correspond to the torque fluctuations of fig. 4 and 5. Fig. 7 shows a lissajous curve of the drive current converted by the clarke transform for a drive method similar to that of fig. 3, except that a modulation ratio of 0.7 is used. Features/details of the graph of fig. 7 are similar to those of fig. 6, except for the plotted values.

When the initial drive modulation ratio for the drive method is less than 100%, two phases (phases other than the current HiZ, the non-excited phase) can be modulated with a ratio greater than the initial modulation ratio to reduce the torque reduction caused by the HiZ window. The motor torque is generated by a q-axis current, and the q-axis current is a vector (stator current vectors of three phases are projected to the q-axis).

As described above, the N-window driving method includes the non-excitation period. In this disclosure, any given phase of the N period or the non-energized period is referred to as a window period, and any given phase of the energized period is referred to as an energized period. For any given phase, the energization period begins at the end of the window period and ends at the beginning of the window period. When any given phase is in the energization period, there are two possible cases. All phases are in the energization period (referred to herein as the allong period) or one phase other than the given phase is in the window period (referred to herein as the wnding period).

As a simple example, returning to fig. 3, it can be seen that at an electrical angle position of pi/3 (about 1.0471976), the V-phase has a negative current, the U-phase has a positive current, and the W-phase is at zero current. From a V-phase or U-phase perspective, this would be a wnding period. At an electrical angle position of pi/6 (about 0.523599), the V-phase has a negative phase current, and the U-phase and the W-phase each have a positive phase current. Therefore, this will be the ALLENG period. Thus, whether a phase is in the "energized/excited state" or the "non-energized/excited state" as those terms are used herein is determined by whether the current of that phase is zero (the non-energized/excited state) or has a non-zero value (the energized/excited state), rather than by whether the phase drive voltage is zero or non-zero. For example, it can be seen in fig. 3 that at an electrical angle position of pi/6 (about 0.523599), the V-phase has a zero drive voltage, while both the U-phase and the W-phase have a positive drive voltage. A zero drive voltage for the V-phase does not mean that the V-phase is not energized because, as defined herein, if the phase current is non-zero, that phase is energized. Similarly, at an electrical angle position of π/3 (about 1.0471976), even though the W-phase has a positive/non-zero voltage, it is non-energized/non-energized because it has zero phase current.

Further, still referring to fig. 3 and also to fig. 32, fig. 32 depicts a circuit diagram of a controller that may be used to control a three-phase motor and ignore Rs resistance, at an electrical angle position of pi/3 (about 1.0471976), Q1H and Q1L of the inverter are switched using Pulse Width Modulation (PWM), Q2H is off and Q2L is on, and Q3H and Q3L are off. Thus, UOUT outputs non-zero volts, VOUT outputs zero volts, and WOUT outputs the HiZ state. Since PWM is performed with synchronous rectification and the stator of the motor is an inductive load, there is a resulting current and a regenerative current (the zero volt/zero drive node can also act as a sink node for another source node). During this angular position, although VOUT outputs zero volts, IV (V phase current) flows via the U phase (meaning UOUT is the source node and VOUT is the sink node). Therefore, even if VOUT outputs zero volts during this period, the V phase of the motor is energized via the U phase. However, in this same period, even if WOUT has a positive voltage, IW (W-phase current) does not flow because its positive voltage is not based on the drive voltage output by WOUT, and thus the W-phase is not energized. The node voltage during the non-energization period indicates the generated voltage (impedance from the other two phases) and has a value of the sum of the voltages of the other two phases divided by half. The BEMF voltage overlaps this period, but for simplicity, as shown, is not included in the figure.

Referring now to fig. 8, there is shown a schematic diagram illustrating control of the U-phase in a method of driving a three-phase motor. The graph depicts the voltage drive amplitude of the phase plotted against the electrical angle of the rotor (in radians). Referred to at the top of the figure as the "window period of self-phase" portion, which is the window period of the U-phase, or in other words, the period in which the U-phase may be in the HiZ state (with zero phase current) to perform BEMF detection. An "energization period" portion is also labeled, which indicates a period in which the U-phase has a non-zero phase current (even if the drive voltage is zero) so that the U-phase is "energized". The energization period is also shown alternating between an ALLENG period, in which all phases are energized, and a WNDENG period, in which another phase (one other) is not energized (e.g., each phase in three phases is not energized). In this example, there are six windows: two for the U-phase itself (the first and last window periods are half of a single window), two for the W-phase, and two for the V-phase. Thus, each segment represents 30 degrees of rotation of the rotor. Similar plots can be made to control the V and W phases. The figure is an example of controlling the phase in a 6-window mode.

The graph of fig. 8 represents control of the U-phase without changing the voltage during the wnding period, and therefore there will be torque ripple discussed above. On the other hand, fig. 9 shows a similar graph for the U-phase in a 6-window mode with a 30 degree window, but where the voltage applied to the U-phase is temporarily switched from a sinusoidal waveform to a different waveform when a positive voltage is applied to the U-phase and when the WNDENG window is reached. This different waveform causes the voltage of the U-phase to increase. In this example, the modulation ratio is 1.0. The HiZ period/window for the U phase is also shown in the graph. The ALLENG period of the U-phase is controlled based on the first 2-phase modulation waveform, and the WNDENG period of the U-phase is controlled by the second 2-phase modulation waveform. In implementations, the second 2-phase modulation waveform may be a processed or modified version of the first waveform, or it may be an entirely different waveform that is not based on the first waveform. In either case, the second waveform (and, in general, the different waveform during the wnding period) is referred to herein as a Low Torque Ripple (LTR) modulation waveform because they reduce torque ripple. While the graph of fig. 9 focuses on the U-phase, the graphs depicting control/drive voltages for the V-phase and W-phase would be similar (but offset by 120 and 240 degrees, respectively, from the U-phase).

Fig. 10 is a schematic diagram showing control of the U-phase in the method of driving the three-phase motor, and is similar to fig. 9 except that a modulation ratio of 0.7 is used. Likewise, when a positive voltage is applied to the U-phase and reaches the WNDENG window, the voltage applied to the U-phase is temporarily switched from a sinusoidal waveform to a different waveform (LTR waveform). It can be seen that the LTR waveform is different from the LTR waveform of the 1.0 modulation ratio version of figure 9, but still generally results in an increase in voltage within at least a portion of the wnding period compared to the voltage applied using the original sine wave function. It can be seen that the applied voltage remains zero for the wnding period with zero applied voltage for the U-phase. However, at these wnding windows, the voltage applied to the other phases may be increased to reduce torque ripple. While the graph of fig. 10 focuses on the U-phase, the graphs depicting control/drive voltages for the V-phase and W-phase would be similar (but offset by 120 and 240 degrees, respectively, from the U-phase).

The LTR waveform used during the wnding window reduces the torque dip at the HiZ window. Therefore, even if one of the three phases of the motor stator is in a non-excited state, the reduction in torque is not as large as it is. The alternative LTR waveform is therefore defined such that torque fluctuations are reduced. In a specific implementation, when one phase is not excited, the other two phases are excited and driven by replacing the normal sinusoidal drive value with the LTR drive value. In other implementations, when one phase is not actuated, the other two phases are actuated but only one of the phases is driven by replacing the normal sinusoidal drive value with the LTR drive value. In the embodiments described and illustrated herein, alternative drive values are applied to the wye-connected stator. However, in other implementations, the principles and methods disclosed herein may be adapted for use with other types of electric machines. As shown, the graphs of fig. 9 and 10 have 6 wnding windows. This is the maximum window amount per electrical angle period of the rotor for replacing the normal sinusoidal drive value with the LTR drive value. The zone width is defined to within +/-30 degrees centered at the zero crossing of the phase BEMF.

Fig. 11 shows a schematic diagram illustrating control of the U-phase in a method of driving a three-phase motor in a 3-window mode having a 30-degree window. When a positive voltage is applied to the U-phase and reaches the WNDENG window, the voltage applied to the U-phase is temporarily switched from the sinusoidal waveform to the LTR waveform. The LTR waveform causes the drive voltage to increase within at least a portion of the wnding period relative to a normal sinusoidal drive waveform. When the wnding window ends, the voltage applied to the U-phase switches back to the normal sinusoidal waveform. In this example, the modulation ratio is 1.0. The HiZ period/window for the U phase is also shown in the graph. While the graph of fig. 11 focuses on the U-phase, the graphs depicting control/drive voltages for the V-phase and W-phase would be similar (but offset by 120 and 240 degrees, respectively, from the U-phase).

Fig. 12 is a schematic diagram showing control of the U-phase in the method of driving the three-phase motor, and is similar to fig. 11 except that a modulation ratio of 0.7 is used. Likewise, when a positive voltage is applied to the U-phase and when the WNDENG window is reached, the voltage applied to the U-phase is temporarily switched from the sinusoidal waveform to the LTR waveform. When the wnding window ends, the voltage applied to the U-phase switches back to the normal sinusoidal waveform. It can be seen that the LTR waveform is different from the LTR waveform of the 1.0 modulation ratio version of figure 11, but still generally results in an increase in voltage within at least a portion of the wnding period compared to the voltage applied using the original sine wave function. It can be seen that the applied voltage remains zero for the wnding period with zero applied voltage for the U-phase. However, at these wnding windows, the voltage applied to the other phases may be increased to reduce torque ripple. While the graph of fig. 12 focuses on the U-phase, the graphs depicting control/drive voltages for the V-phase and W-phase would be similar (but offset by 120 and 240 degrees, respectively, from the U-phase).

Fig. 13 shows a schematic diagram illustrating control of the U-phase in a method of driving a three-phase motor in a 2-window mode having a 30-degree window. In this case, there is no wnding window because in the 2-window mode, the V-phase and W-phase do not have a HiZ window/period. Thus, the U-phase is controlled by a normal sinusoidal waveform without any LTR waveform.

However, fig. 14 shows a schematic diagram illustrating control of the V phase in a method of driving a three-phase motor in a 2-window mode having a 30-degree window. When a positive voltage is applied to the V-phase and reaches the WNDENG window (HiZ window for the U-phase), the voltage applied to the V-phase is temporarily switched from the sinusoidal waveform to the LTR waveform. The LTR waveform causes the drive voltage to increase within at least a portion of the wnding period relative to a normal sinusoidal drive waveform. When the wnding window ends, the voltage applied to the V phase switches back to the normal sinusoidal waveform. In this example, the modulation ratio is 1.0. The graph also shows that the V-phase does not have a HiZ period/window. While the graph of fig. 14 focuses on the V-phase, the graph depicting the control/drive voltage for the W-phase would be similar (but shifted 120 degrees from the V-phase).

Fig. 15 is a schematic diagram showing control of the V-phase in the method of driving the three-phase motor, and is similar to fig. 14 except that a modulation ratio of 0.7 is used. Likewise, when a positive voltage is applied to the V-phase and reaches the WNDENG window (HiZ window for the U-phase), the voltage applied to the V-phase is temporarily switched from the sinusoidal waveform to the LTR waveform. When the wnding window ends, the voltage applied to the V phase switches back to the normal sinusoidal waveform. It can be seen that the LTR waveform is different from the LTR waveform of the 1.0 modulation ratio version of figure 14, but still generally results in an increase in voltage within at least a portion of the wnding period compared to the voltage applied using the original sine wave function. It can be seen that the applied voltage remains zero for the wnding period with zero applied voltage for the V phase. However, at these wnding windows, the voltage applied to the W phase may be increased to reduce torque ripple. While the graph of fig. 15 focuses on the V-phase, the graph depicting the control/drive voltage for the W-phase would be similar (but shifted 120 degrees from the V-phase).

Fig. 16 shows a schematic diagram illustrating control of the U-phase in a method of driving a three-phase motor in a 1-window mode having a 30-degree window. In this case, there is no wnding window because in the 1-window mode, the V-phase and W-phase do not have the HiZ window/period. Thus, the U-phase is controlled by a normal sinusoidal waveform without any LTR waveform.

Fig. 17 shows a schematic diagram illustrating control of the V phase in a method of driving a three-phase motor in a 1-window mode having a 30-degree window. In this case, there is a wnding window, but it does not correspond to a positive voltage applied to the V-phase, so the V-phase is not modified from its normal sinusoidal waveform. The modulation ratio in fig. 17 is 1.0. No figure is provided showing the control of the W phase in the method of driving the three-phase motor in the 1-window mode having the 30-degree window, but the W phase will be shifted from the V phase by 120 degrees so that the positive voltage applied to the W phase will overlap the wnding window of the U phase. Thus, during the wnding window, the W phase will be driven by the LTR waveform, which will result in an increased applied voltage relative to the normal sinusoidal waveform for at least a portion of the wnding period. After the wnding period has elapsed, the W phase will return to the normal sinusoidal waveform. Qualitatively, the voltage difference applied to the W-phase during the wnding period between the 1.0 modulation ratio and the 0.7 modulation ratio would be similar to the voltage difference applied to the V-phase during the wnding period between the 1.0 modulation ratio and the 0.7 modulation ratio shown in fig. 14 and 15.

There is a limit to the window period for each phase. The limits of the window period (in degrees) can be seen in table 1 below.

TABLE 1

Fig. 18 shows the maximum window period of the three phases when a modulation ratio of 1.0 is used and when the LTR waveform is not used. The different cross-hatched portions reflect the windows. For example, the W phase is considered to have a first window between 30 and 90 degrees. This is about 0.52 radians to 1.57 radians in radians. Thus, on the graph of fig. 18, there is a first W portion in which the letter W is close to the W curve, but also within a first cross-hatched portion from the left side of the graph, which has a line sloping downward toward the right side. The W portion is shown between about 0.52 radians and about 1.57 radians, corresponding to 30 degrees and 90 degrees. The next W portion (with similar cross-hatching) is shown between 210 and 270 degrees (but in fig. 18, in arches). Fig. 19 similarly shows the maximum window period of the three phases when a modulation ratio of 1.0 is used and when LTR waveforms are used. Fig. 20 shows the maximum window period of three phases when the modulation ratio is 0.7 and the LTR waveform is used. If the BEMF zero-crossing cannot be detected before the end of the limitation as shown in Table 1, the HiZ state ends according to the limitation of the window period. In this case, to continue operation, interpolation will be performed by the "rotor position/speed generator" block of the system (shown in FIG. 37).

Representative examples of the drive functions for the three phases in embodiments using LTR modulation are given below.

In the above formula, some values are calculated as follows:

the variables in the above formula are defined as follows:

U_2pm: u phase 2 phase modulation waveform (fundamental wave of N window method)

V_2pm: v phase 2 phase modulation waveform (fundamental wave of N window method)

W_2pm: w-phase 2-phase modulation waveform (fundamental wave of N-window method)

U_3pm: u-phase 3-phase modulation waveform

V_3pm: v-phase 3-phase modulation waveform

W_3pm: w-phase 3-phase modulation waveform

U_ltrm: u-phase modulation waveform [ Low Torque Ripple (LTR) modulation during window]

V_ltrm: v-phase modulation waveform [ Low Torque Ripple (LTR) modulation during window]

W_ltrm: w-phase modulation waveform [ Low Torque Ripple (LTR) modulation ] during window]

θ: rotor position in electrical angle

M: modulation ratio (0 to 1)

In this representative example, a normal sinusoidal waveform will result in a reduction in torque when one of the three phases is in the window period. Thus, LTR modulation is applied during the window to reduce torque ripple. In practice, the LTR modulation should be operated with consideration to the transfer function of the motor stator, but this is omitted herein to simplify and highlight other aspects of LTR modulation. Table 2 below gives the U for different values of theta_ltrm、V_ltrmAnd W_ltrmThe modulation ratio of (2).

Theta (degree)	Ultrm	Vltrm	Wltrm
					0≤θ<30	HiZ	0	Mltr
30≤θ<90	M ltr	0	HiZ
				90≤θ<150	Mltr	HiZ	0
150≤θ<210	HiZ	M	ltr					0
				210≤θ<270	0	Mltr	HiZ
270≤θ<330	0	HiZ	Mltr
				330≤θ<360	HiZ	0	Mltr

TABLE 2M in this representative example_ltrThe values are given by the following equations.

In the above formula, M is a modulation ratio ranging from 0 to 1And theta_wcIs the center phase position of the maximum window period, which is given by table 3 below.

Theta (degree)	θwc(degree)
		0≤θ<30	0
30≤θ<90	60
		90≤θ<150	120
150≤θ<210	180
		210≤θ<270	240
270≤θ<330	300
		330≤θ<360	0

TABLE 3

Fig. 21 shows a vector diagram of a current vector in LTR modulation. In this example, "d" represents the d-axis of the rotor and "q" represents the q-axis of the rotor. For this graph, it is assumed that the stator of the motor is configured by a star connection, the resistance of each phase is 1 ohm, and the rotor position is 0 ≦ θ <30 or 330 ≦ θ < 360.

Fig. 22 shows a graph of voltage and current magnitude plotted as a function of electrical angular position of the rotor for a specific implementation of a method of driving a three-phase motor including LTR modulation. For simplicity, the graph omits the stator inductance and BEMF voltage. The drive phase voltages and drive phase currents are shown and the characteristics/details of the graph are similar to those of fig. 1 except for the values plotted. A modulation ratio of 1.0 is used in this driving method.

When a positive voltage is applied to a phase and reaches the WNDENG window, the voltage applied to that phase is temporarily switched from the sinusoidal waveform to the LTR waveform. The LTR waveform causes the drive voltage to increase within at least a portion of the wnding period relative to a normal sinusoidal drive waveform. When the wnding window ends, the voltage applied to the phase switches back to the normal sinusoidal waveform. The HiZ period/window for each phase is also visible in the graph.

Fig. 23 shows a graph of voltage and current magnitude plotted as a function of electrical angular position of the rotor for a specific implementation of a method of driving a three-phase motor including LTR modulation. The graph is similar to fig. 22, except that a modulation ratio of 0.7 is used. For simplicity, the graph omits the stator inductance and BEMF voltage. The drive phase voltages and drive phase currents are shown and the characteristics/details of the graph are similar to those of fig. 1 except for the values plotted. When a positive voltage is applied to a phase and reaches the WNDENG window, the voltage applied to that phase is temporarily switched from the sinusoidal waveform to the LTR waveform. It can be seen that the LTR waveform for the 0.7 modulation ratio is different from the LTR waveform for the 1.0 modulation ratio, but still results in an increase in drive voltage over at least a portion of the wnding period relative to the normal sinusoidal drive waveform. When the wnding window ends, the voltage applied to the phase switches back to the normal sinusoidal waveform. The HiZ period/window for each phase is also visible in the graph.

In the examples of FIGS. 22-23, the electrical angular position and the width of the window period are 0 degrees +/-15 degrees, 60 degrees +/-15 degrees, 120 degrees +/-15 degrees, 180 degrees +/-15 degrees, 240 degrees +/-15 degrees, and 300 degrees +/-15 degrees.

Fig. 24 representatively illustrates torque of the three-phase motor of fig. 22 plotted against electrical degrees (this time in degrees) of the rotor of the motor. The torque is represented by a q-axis current converted by the clark-park transformation, which represents the torque produced. The torque ripple can be seen in fig. 24, where the torque drops very low in several places, each of these drops corresponding to the HiZ window of one of the phases. The torque fluctuations are improved relative to the torque fluctuations of fig. 4, but they are still present.

Fig. 25 representatively illustrates torque of the three-phase motor of fig. 23 plotted against electrical degrees (this time in degrees) of the rotor of the motor. The torque is represented by a q-axis current converted by the clark-park transformation, which represents the torque produced. In this graph, torque ripple is no longer seen. Thus, the graph is an example of a graph plotting the generated torque of the three-phase motor on the y-axis and the rotor angular position of the rotor of the three-phase motor on the x-axis, showing that the generated torque (the single torque value after 360 degrees of rotation through the electric drive) does not change in at least one 360 degrees of rotation of the rotor through the electric drive. This shows that, with the LTR modulation equation given above, when the modulation ratio M is 1, the torque ripple remains unchanged, but when the modulation ratio M is reduced to 0.7, the ripple is sufficiently reduced so as not to appear on the graph of fig. 25. In particular implementations, modulation ratios higher than 0.7 may also result in a significant reduction in torque ripple, sufficient to present a graph similar to that of fig. 25. It is also expected that modulation ratios below 0.7 will produce a graph similar to fig. 25 showing no torque ripple.

The reduction in torque ripple may result in increased life of the motor, reduced wear of the motor and its components, quieter operation, more efficient operation, and the like. As a non-limiting example, in fan motor applications, a smaller modulation ratio will generally mean lower speed operation of the motor, and in this case it also results in lower torque ripple, thereby reducing fan vibration and noise.

Fig. 26 shows lissajous curves for drive current converted by the clarke transform for the drive method of fig. 22 using a modulation ratio of 1.0. The I-Alpha axis is Alpha axis current and the I-Beta axis is Beta axis current. The lissajous curve shows the position of the torque when current is applied and the motor is applied. At locations on the curve where there are no circles, this indicates that the torque jumps from one value to another — these locations correspond to the torque fluctuations of fig. 24. Fig. 27 shows lissajous curves for drive current converted by the clarke transform for the drive method of fig. 23 using a modulation ratio of 0.7. Features/details of the graph of fig. 27 are similar to those of fig. 26, except for the plotted values. However, although there is a position without a circle, the torque fluctuation is not obvious in the graph of fig. 25. These lissajous curves also show that the drive current value itself varies between the TR-modulated version and the non-TR-modulated version when compared to the graphs of fig. 6 and 7.

Lead angle control will now be discussed. The lead angle control adds an offset into the phase position to generate a modified drive voltage waveform. For example, when LTR modulation as described above is used and when a modulation ratio of 0.7 is used, then when the lead angle is 0, the generated drive voltage waveform as shown in fig. 23 will be given. On the other hand, if the lead angle amount is changed to 15 degrees, a drive waveform as shown in fig. 28 is generated. Fig. 23 and 28 are both plotted on the assumption that 0 radians is the point at which the U-phase rises above the BEMF zero crossing.

Therefore, when considering the lead angle, the above-mentioned U should be realized in consideration of the amount of the lead angle_2pm、V_2pmAnd W_2pmAnd (4) a formula. However, tables 2 and 3 and M above_ltrThe formula should be implemented by theta information without considering the lead angle. This means that the θ information used to determine the basic 2-phase modulation waveform should include the lead angle amount, but the window period and LTR modulation should operate by the θ information that does not include the lead angle amount.

Referring now to fig. 29, another example of a graph of voltage and current magnitude plotted as a function of electrical angular position of the rotor for a specific implementation of a method of driving a three-phase motor (including LTR modulation) is shown. This method differs from the method and formula disclosed above in that the LTR modulation phase returns to the normal sinusoidal phase (whole) upon detection of BEMF, rather than being driven by LTR modulation for the entire wnding window. In particular implementations, this further improves efficiency and reduces torque ripple to reduce noise, extend motor life, and reduce wear, among other things. The example in fig. 29 uses a modulation ratio of 0.6 and shows a HiZ window. Features/details of fig. 29 are similar to those of fig. 1, except for the plotted values. In another representative example, a predetermined time may be selected and LTR modulation may be used to drive the phase voltages only up to the predetermined time, the predetermined time being selected to be sufficient to detect BEMF, but still only a fraction of the entire wnding window.

In the implementation of fig. 29, the electrical angular position and width of the window period are 0 degrees +0/-15 degrees, 60 degrees +0/-30 degrees, 120 degrees +0/-15 degrees, 180 degrees +0/-15 degrees, 240 degrees +0/-15 degrees, and 300 degrees +0/-15 degrees.

Fig. 30 representatively illustrates torque of the three-phase motor of fig. 29 plotted against the electrical angle (in degrees) of the rotor of the motor. The torque is represented by a q-axis current converted by the clark-park transformation, which represents the torque produced. In this graph, no torque fluctuation is observed again. Thus, the graph is another example of a graph plotting the generated torque of a three-phase motor on the y-axis and the rotor angular position of the rotor of the three-phase motor on the x-axis, the graph showing no change in the generated torque over 360 degrees of rotation of at least one electric drive of the rotor.

Fig. 31 shows lissajous curves of drive current converted by the clarke transform for the drive method of fig. 29. Features/details of the graph of fig. 31 are similar to those of fig. 27, except for the plotted values. However, although there is a position without a circle, the torque fluctuation is not obvious in the graph of fig. 30. The lissajous curve also shows that the drive current value varies between the TR-modulated version and the non-TR-modulated version when compared to the graph of fig. 7.

Referring now to fig. 32, an example of a three-phase inverter circuit that may be used in or with a control module to control a three-phase motor according to the methods disclosed herein is shown. A three-phase inverter circuit uses three half-bridges to drive a motor. As an example of driving only the U-phase, when a driving voltage is applied to the U-phase, the UH is pulsed on and off using PWM. When UH is on, UL is off, and vice versa. When the drive voltage of the U-phase is zero, UL remains on and UH remains off.

Referring now to fig. 33, a block diagram representatively illustrates a controller (which may be implemented in an integrated circuit, in certain embodiments) that controls a three-phase motor using the methods disclosed herein. Various elements are shown including encoder modules/components, LTR (low torque ripple) modulation modules/components, 2-phase modulation modules/components, etc. The Pulse Width Modulation (PWM) module is not shown, but representatively shows the electrical connections to be coupled with the PWM module.

The inputs to the controller of fig. 33 include the following: CLK (operation clock); RSTX (reset-0 is reset and 1 is active); RPOS [9:0](rotor position information- θ) (rotor position information based on detected BEMF zero crossing signal, 0.352 degrees/LSB); LA 7:0](lead angle quantity/value-theta)_la) (0.352 degrees/LSB); m [9:0]](output modulation ratio-M, 100% full scale, 0 is 0%); HIZU (non-excitation window period status flag of U phase, 1: window period, 0: normal); HIZV (non-excited window period status flag of V phase, 1: window period, 0: normal); HIZW (non-excitation window period status flag of W phase, 1: window period, 0: normal); CALCUPD (update event flag used to calculate the next value-when the flag goes high, the next value is updated by the input value at that time).

The outputs of the controller of fig. 33 include the following: DRVDUTYU [9:0] (drive PWM duty cycle, U phase, full scale 100%, 0 is 0%); DRVDUTYV [9:0] (drive PWM duty cycle, V phase, full scale 100%, 0 is 0%); DRVDUTYW [9:0] (drive PWM duty cycle, W phase, full scale 100%, 0 is 0%);

RPOSLA is also noted as RPOS + LA. WNDENGU, WNDENGV, and WNDENGW correspond to WNDENG windows of U-phase, V-phase, and W-phase, respectively. The HIZU, HIZV and HIZW are provided by an external module. A PWM module, not shown in fig. 33 but coupled to the controller, is used to complete the full N-window drive waveform including the non-energized phase.

Referring now to fig. 34-36, a number of timing diagrams are presented. The computation of these timing functions must be done within one driving PWM period. TCALC shown in fig. 34 to 36 represents a calculation time, and should be determined according to a practical design. The period of the CALCUPD should match the driving PWM carrier period, but the assertion timing should be optimally designed within the PWM carrier period to minimize system delay with respect to the RPOS and LA information. This means that TCALC is important to optimize the design to ensure that the timing corresponding to the driving PWM carrier period is established.

Fig. 34 is an example of a timing chart in the case where HIZU is 1 and 0 ≦ θ <30 or 330 ≦ θ < 360. In the case of 150 ≦ θ <210, the timing is similar to FIG. 34 as long as the DRVDUTYV output alternates with LTR modulation and the DRVDUTYW output alternates with 2-phase modulation.

Fig. 35 is an example of a timing chart in the case where HIZU is 1 and 90 ≦ θ < 150. In the case of 270 ≦ θ <330, the timing is similar to FIG. 35 as long as the DRVDUTYW output alternates with LTR modulation and the DRVDUTYU output alternates with 2-phase modulation.

Fig. 36 is an example of a timing chart in the case where HIZW is 1 and 210 ≦ θ < 270. In the case of 30 ≦ θ <90, the timing is similar to FIG. 36 as long as the DRVDUTYU output alternates with LTR modulation and the DRVDUTYV output alternates with 2-phase modulation.

Fig. 37 is a block diagram representatively illustrating a three-phase motor and elements for controlling the three-phase motor and detecting the BEMF signal. In this representative example, the three-phase inverter and the BEMF detector are separate individual modules, and all components to the left of these modules are implemented on a single semiconductor device. In this example, the LTR modulation method disclosed herein is implemented using a "2-phase modulation with LTR modulation" block. The configuration of fig. 37 is only applicable to three-phase motors in a star configuration.

In a specific implementation, the modulation ratios disclosed herein may be determined by system capacity, where a modulation ratio of 1.0 is full system capacity (of the applied voltage) and a lower modulation ratio is a corresponding percentage of full system capacity.

It should be noted that table 2 includes values for the 6-window mode only. However, U_2pm、V_2pm、W_2pmThe formula takes precedence over table 2. When the 1-window, 2-window, or 3-window mode is used, the ALLENG period increases within the 6-window ALLENG period, and the WNDENG period and window period decrease. Therefore, LTR modulations can be defined based on the values of table 2, even though they only represent 6 window patterns technically.

It is also noted that the start time of the non-energized portion may be decided according to the corresponding application, and the end time of the non-energized portion may be decided adaptively (or using a predetermined time). When the start time is farther from the BEMF zero crossing, the robustness for detection will improve, but the torque ripple will not be reduced that much.

In various method implementations, the three-phase motor may include a sensorless brushless dc motor and a permanent magnet synchronous motor.

In various method implementations, the method may include driving the second phase using the first sinusoidal drive function after driving the second phase using the second row function until the first BEMF voltage is detected.

In various method implementations, the method may include driving the second phase using the first sinusoidal drive function after driving the second phase using the second drive function for a predetermined amount of time.

In various method implementations, the method can further include: driving a second phase of the three-phase motor using a second sinusoidal drive function when all three phases are energized; driving the second phase using the first non-sinusoidal drive function during at least a portion of the time when a phase other than the second phase is not energized and when the first non-sinusoidal drive function produces a modulation ratio less than 1; and driving the second phase to a modulation ratio of 1 during at least a portion of the time when a phase other than the second phase is not energized and when the first non-sinusoidal drive function produces a modulation ratio greater than or equal to 1.

In various process implementations, theThe method may further include a case where the modulation ratio is a low torque ripple modulation ratio, where the second sinusoidal drive function is

Wherein

Where M is a modulation ratio of 0 to 1, and where θ is a rotation angle of the three-phase motor.

In various method implementations, the method can further include: driving a third phase of the three-phase motor using a third sinusoidal drive function when all three phases are energized; driving a third phase using a first non-sinusoidal drive function during at least a portion of when a phase other than the third phase is not energized and when the first non-sinusoidal drive function produces a modulation ratio less than 1; and driving the third phase to a modulation ratio of 1 for at least a portion of the time when a phase other than the third phase is not energized and when the first non-sinusoidal drive function produces a modulation ratio greater than or equal to 1.

In various method implementations, the method may further include where the modulation ratio is a low torque ripple modulation ratio, where the third sinusoidal drive function is

Wherein

Where M is a modulation ratio of 0 to 1, and where θ is a rotation angle of the three-phase motor.

Where in the above description reference is made to specific implementations of drive methods for three-phase motors and to implementing components, sub-components, methods and sub-methods, it should be readily apparent that various modifications may be made without departing from the spirit thereof, and that these implementations, implementation components, sub-components, methods and sub-methods may be applied to other drive methods for three-phase motors.

Claims (10)

1. A method of driving a wye-connected three-phase electric machine, the method comprising:

driving a second phase of the three-phase motor using a first sinusoidal drive function when a first phase of the star-connected three-phase motor is in an energized state;

switching the first phase to a non-energized state;

detecting a first back electromotive force (BEMF) voltage of the first phase when the first phase is in the non-energized state; and

driving the second phase using a second drive function different from the first sinusoidal drive function for at least a portion of the time that the first phase is in the non-energized state.

2. The method of claim 1, wherein driving the second phase using the second drive function results in an increase in voltage applied to the second phase relative to driving the second phase using the first sinusoidal drive function.

3. The method of claim 1, further comprising: driving a third phase of the three-phase motor using a third drive function different from the second sinusoidal drive function when the first phase is in a second non-energized state, and wherein driving the third phase using the third drive function results in an increase in voltage applied to the third phase relative to driving the third phase using the second sinusoidal drive function.

4. The method of claim 1, wherein plotting the generated torque of the three-phase electric machine on the y-axis and plotting the rotor angular position of the rotor of the three-phase electric machine on the x-axis shows no change in the generated torque over 360 degrees of rotation of the rotor for at least one electric drive.

5. A method of driving a wye-connected three-phase electric machine, wherein the method comprises:

driving a first phase of the star-connected three-phase motor using a first sinusoidal drive function when all three phases are energized;

driving a first phase other than the first phase using a first non-sinusoidal drive function during at least a portion of the time when the first phase is not energized and the first non-sinusoidal drive function produces a modulation ratio less than 1; and

driving the first phase to a modulation ratio of 1 during at least a portion of the time when a phase other than the first phase is not energized and the first non-sinusoidal drive function produces a modulation ratio greater than or equal to 1.

6. The method of claim 5, wherein the first non-sinusoidal drive function is a first cosine drive function.

7. The method of claim 6, wherein:

the modulation ratio is a low torque ripple modulation ratio, wherein the first cosine drive function is

Wherein M is a modulation ratio of 0 to 1, wherein θ is a rotation angle of the three-phase motor, and wherein when θ is less than 30 degrees and greater than or equal to 0 degrees, θ_wcHas a value of 0 degrees; when theta is less than 90 degrees and greater than or equal to 30 degrees, theta_wcHas a value of 60 degrees; when theta is less than 150 degrees and greater than or equal to 90 degrees, theta_wcHas a value of 120 degrees; when theta is less than 210 degrees and greater than or equal to 150 degrees, theta_wcHas a value of 180 degrees; when theta is less than 270 degrees and greater than or equal to 210 degrees, theta_wcHas a value of 240 degrees; when theta is less than 330 degrees and greater than or equal to 270 degrees theta_wcHas a value of 300 degrees; and when theta is less than 360 degrees and greater than or equal to 330 degrees theta_wcHas a value of 0 degrees; and is

Wherein the modulation ratio is a low torque ripple modulation ratio, wherein the first sinusoidal drive function is

Wherein

Wherein M is a modulation ratio of 0 to 1, and wherein θ is a rotation angle of the three-phase motor.

8. A method of driving a three-phase electric motor, the method comprising:

when all three phases are energized, driving the U phase of the three-phase motor by using a first sinusoidal driving function;

when all three phases are electrified, driving the V phase of the three-phase motor by using a second sinusoidal driving function;

when all three phases are energized, driving the W phase of the three-phase motor using a third sinusoidal drive function; and

during a period in which one of the three phases is not energized, driving the two remaining energized ones of the three phases using a cosine drive function for at least a portion of the period.

9. The method of claim 8, further comprising: driving the energized remaining two of the three phases with the cosine drive function during a period when one of the three phases is not energized and for at least a portion of the time when the cosine drive function produces a modulation ratio less than 1, and driving the energized remaining two of the three phases to a modulation ratio of 1 during a period when one of the three phases is not energized and for at least a portion of the time when the cosine drive function produces a modulation ratio greater than or equal to 1.

10. The method of claim 9, wherein:

the modulation ratio is a low torque ripple modulation ratio, wherein the cosine drive function is

Wherein M is a modulation ratio of 0 to 1, wherein θ is a rotation angle of the three-phase motor, and wherein θ_wcA value of 0 degree when θ is less than 30 degrees and greater than or equal to 0 degree, a value of 60 degrees when θ is less than 90 degrees and greater than or equal to 30 degrees, a value of 120 degrees when θ is less than 150 degrees and greater than or equal to 90 degrees, a value of 180 degrees when θ is less than 210 degrees and greater than or equal to 150 degrees, a value of 240 degrees when θ is less than 270 degrees and greater than or equal to 210 degrees, a value of 300 degrees when θ is less than 330 degrees and greater than or equal to 270 degrees, and a value of 0 degrees when θ is less than 360 degrees and greater than or equal to 330 degrees; and is

Wherein the modulation ratio is a low torque ripple modulation ratio, wherein the first sinusoidal drive function is

Wherein the second sinusoidal drive function is

Wherein the third sinusoidal drive function is

Wherein

Wherein M is a modulation ratio of 0 to 1, and wherein θ is a rotation angle of the three-phase motor.

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